

where \(D\)  is the Hirota bilinear operator defined as [1]}
\(D_x^mD_t^n\ f\cdot g\equiv (\partial _x -\partial _{x^{\prime }})^m (\partial _t-\partial _{t^{\prime }})^nf(x,t) g(x^{\prime },t^{\prime })|_{x^{\prime }=x,t^{\prime }=t}.\) 
